I'm not reversing the math. They increase the workload by 1/3 of your prediction, so you give them a prediction which is sized such that, after adding the current workload to the increase based on your prediction, you get the prediction.

It'd be 1/2 your prediction, if you're giving them 10 days and want to arrive at 15 after they add their increase. Doesn't actually matter, though, you made your point clear.

And you don't need to predict the next round of mugging because the idea is to give a prediction which takes into account all successive rounds of mugging. If the sum of all these rounds is greater than 100%, the problem can never end at all. If it's less, you can do what I said.

They're adjusting their mugging so that it's always more profitable for you to continue than stop, if you discount what you've already spent. They've anticipated your predictions, and have priced accordingly.

That's assuming they want to maximize their mugging. They could execute only one or two muggings, and you might not catch on at all.